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MSSM flat direction as a curvaton

Kari Enqvist, Asko Jokinen, Shinta Kasuya, Anupam Mazumdar

TL;DR

This work evaluates whether MSSM flat directions can serve as curvatons to produce the observed adiabatic perturbations. It analyzes the flat-direction potential, the role of nonrenormalizable terms, Hubble-induced masses, and perturbation evolution in both visible- and hidden-sector inflaton scenarios, identifying stringent conditions for late-time domination and perturbation survival. The key finding is that, in most setups, damping of fluctuations or thermal effects prevents successful curvaton domination, with a narrow viable possibility for the $n=9$ direction under specific initial conditions in a hidden-inflation framework; fragmentation into $Q$-balls in no-scale SUGRA further complicates the picture. Overall, while MSSM flat directions as curvatons are not ruled out, they require finely-tuned dynamics or particular symmetries, and their realization remains highly model-dependent and challenging.

Abstract

We study in detail the possibility that the flat directions of the Minimal Supersymmetric Standard Model (MSSM) could act as a curvaton and generate the observed adiabatic density perturbations. For that the flat direction energy density has to dominate the Universe at the time when it decays. We point out that this is not possible if the inflaton decays into MSSM degrees of freedom. If the inflaton is completely in the hidden sector, its decay products do not couple to the flat direction, and the flat direction curvaton can dominate the energy density. This requires the absence of a Hubble-induced mass for the curvaton, e.g. by virtue of the Heisenberg symmetry. In the case of hidden radiation, $n=9$ is the only admissible direction; for other hidden equations of state, directions with lower $n$ may also dominate. We show that the MSSM curvaton is further constrained severely by the damping of the fluctuations, and as an example, demonstrate that in no-scale supergravity it would fragment into $Q$ balls rather than decay. Damping of fluctuations can be avoided by an initial condition, which for the $n=9$ direction would require an initial curvaton amplitude of $\sim 10^{-2}M_p$, thereby providing a working example of the MSSM flat direction curvaton.

MSSM flat direction as a curvaton

TL;DR

This work evaluates whether MSSM flat directions can serve as curvatons to produce the observed adiabatic perturbations. It analyzes the flat-direction potential, the role of nonrenormalizable terms, Hubble-induced masses, and perturbation evolution in both visible- and hidden-sector inflaton scenarios, identifying stringent conditions for late-time domination and perturbation survival. The key finding is that, in most setups, damping of fluctuations or thermal effects prevents successful curvaton domination, with a narrow viable possibility for the direction under specific initial conditions in a hidden-inflation framework; fragmentation into -balls in no-scale SUGRA further complicates the picture. Overall, while MSSM flat directions as curvatons are not ruled out, they require finely-tuned dynamics or particular symmetries, and their realization remains highly model-dependent and challenging.

Abstract

We study in detail the possibility that the flat directions of the Minimal Supersymmetric Standard Model (MSSM) could act as a curvaton and generate the observed adiabatic density perturbations. For that the flat direction energy density has to dominate the Universe at the time when it decays. We point out that this is not possible if the inflaton decays into MSSM degrees of freedom. If the inflaton is completely in the hidden sector, its decay products do not couple to the flat direction, and the flat direction curvaton can dominate the energy density. This requires the absence of a Hubble-induced mass for the curvaton, e.g. by virtue of the Heisenberg symmetry. In the case of hidden radiation, is the only admissible direction; for other hidden equations of state, directions with lower may also dominate. We show that the MSSM curvaton is further constrained severely by the damping of the fluctuations, and as an example, demonstrate that in no-scale supergravity it would fragment into balls rather than decay. Damping of fluctuations can be avoided by an initial condition, which for the direction would require an initial curvaton amplitude of , thereby providing a working example of the MSSM flat direction curvaton.

Paper Structure

This paper contains 10 sections, 23 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Flat direction and inflation
  3. Late domination of the flat direction energy density
  4. Evolution of perturbations
  5. Slow rolling in nonrenormalizable potential
  6. Positive Hubble-induced mass term
  7. Negative Hubble-induced mass term
  8. The way out
  9. Fragmentation of the flat direction
  10. Conclusion

Figures (2)

  • Figure 1: Constraint on the coupling for $n=4,6,7$, and 9. The allowed region is below these lines and above $f=10^{-6}$.
  • Figure 2: $K$ vs. $\tan\beta$. On the left $LLdsb$ flat direction with a choice of stau in the flat direction (solid line) and no stau in the flat direction (dashed line). On the right $QuQue$ flat direction with $u$ from 3rd generation (thick lines) and $Q$ from 3rd generation (thin lines), $e$ from 3rd generation (solid line) and $e$ from 1st or 2nd generation (dashed line).